When electromagnetic radiation is incident on a medium, the medium is said to respond to the radiation, producing responding fields and currents. This response is generally determined by the composition, structure, and geometry of the medium. The response may, in general, be quite complicated due to a collection of either homogenous or heterogeneous scattering entities within the medium. However, when the dimensions and spacing of these individual scattering elements comprising the medium are less than the wavelength of the incident radiation, the responding fields and currents can be considered as macroscopic averages, and the medium treated as if it is relatively continuous.
Media typically found in nature or that can be formed by known chemical synthesis, referred to herein as naturally occurring media, generally exhibit a broad, but limited, range of response to electromagnetic radiation. These materials are often referred to as right-handed materials or positive index materials because they exhibit positive values for both electric permittivity and magnetic permeability.
However, some man made materials, often referred to as left-handed materials, meta-materials, or negative index materials, exhibit negative values for both electric permittivity and magnetic permeability. Negative magnetic permeability is not observed in natural materials, especially at frequencies approaching visible range. It however, may exist in meta-materials as a result of collective motion of large number of electrons in response to an incident radiation field. With negative electric permittivity and magnetic permeability, a meta-material may exhibit a refractive index that is negative, thus the name negative index materials. Conversely, naturally occurring media generally exhibit a positive refractive index.
Meta-materials exhibiting a negative refractive index may be useful in new and different ways for modifying electromagnetic radiation in areas such as focusing, transmission, and amplification. Meta-materials comprising a composite media, including a periodic array of conducting elements that behave substantially as a continuous media and exhibit negative refractive properties over a frequency band of interest, have been proposed. However, these proposals have generally been limited to materials that may be fabricated as two dimensional arrays, with multiple two-dimensional arrays being arranged in a pattern to create a three-dimensional structure for the meta-material. This process of arranging two-dimensional arrays and creating three-dimensional structures can be difficult, costly, and often unsuccessful.
Accordingly, there is a need for a more easily fabricated meta-material that exhibits negative refractive properties and which may be more easily fabricated in a three-dimensional volume.